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We present a framework for constructing strong mixed-integer programmingformulations for logical disjunctive constraints. Our approach is ageneralization of the logarithmically-sized formulations of Vielma andNemhauser for SOS2 constraints, and we offer a complete characterization of itsexpressive power. We apply the framework to a variety of disjunctiveconstraints, producing novel small and strong formulations for outerapproximations of multilinear terms, generalizations of special ordered sets,piecewise linear functions over a variety of domains, and obstacle avoidanceconstraints.

A combinatorial approach for small and strong formulations of disjunctive constraints